In this paper, we propose GMMC by reinterpreting the max-Mahalanobis classifier [1]} as an EBM. Compared to the standard softmax classifier utilized in JEM, GMMC models the latent feature space explicitly as the max-Mahalanobis distribution, which aligns well with the generative process of image synthesis. We show that GMMC can be trained discriminative, generatively or jointly with reduced complexity and improved stability compared to JEM. Extensive experiments on the benchmark datasets demonstrate that GMMC can achieve state-of-the-art discriminative and generative performances, and improve calibration, out-of-distribution detection and adversarial robustness.
